We investigate the association between controlling shareholders' ownership (CS_Own) and firms' leverage decisions in the Singaporean context. We examine whether the impact of ownership concentration on leverage differs across excess and lower control. We report that shareholders with excess control prefer leverage financing for an optimal capital structure and focus on value maximisation rather using leverage as a tool of minority shareholders' expropriation. Our analysis shows that firms capital structure significantly influences by the coalition of shareholders particularly decisions about leverage (...) financing in addition to the firms' specific characteristics and institutional arrangements. Our empirical evidence shows that controlling shareholders with a lower fraction of equity are more concerned about limited holding thus prefer leverage over equity financing to inflate their equity stake to protect them from the potential takeovers and mergers. We report that capital structure decisions in Singapore are linked with the trade-off between the controlling shareholders' target of mitigating firm risk and their non-dilution entrenchment needs. Further, we found an inverted U-shaped association between control ownership and leverage financing. In terms of moderating effect of family-controlled ownership, our findings exhibit that leverage financing is less pronounced for family firms in Singapore due to the under-diversified investment portfolio. (shrink)

We investigate the firms’ specific attributes that determine the difference in speed of adjustment (SOA) towards the cash holdings target in the Scandinavian countries: Denmark, Norway and Sweden. We examine whether Scandinavian firms maintain an optimal level of cash holdings and determine if the active cash holdings management is associated with the firms’ higher SOA and lower adjustment costs. Our findings substantiate that a higher level of off-target cost induces professional managers to rebalance their cash level towards the optimal balance (...) of cash holdings. Our results reveal that Scandinavian firms accelerate SOA towards cash targets primarily for the precautionary motive. Moreover, our results show that SOA is heterogeneous across Scandinavian firms based on adjustment cost and deviate cash holdings towards the target mainly with the support of internal financing. Furthermore, our empirical findings show that the SOA of Norwegian firms is significantly higher than the Danish and Swedish firms. (shrink)

A holobiont is a composite organism consisting of a host together with its microbiome, such as a coral with its zooxanthellae. To explain the often intimate integration between hosts and their microbiomes, some investigators contend that selection operates on holobionts as a unit and view the microbiome’s genes as extending the host’s nuclear genome to jointly comprise a hologenome. Because vertical transmission of microbiomes is uncommon, other investigators contend that holobiont selection cannot be effective because a holobiont’s microbiome is an (...) acquired condition rather than an inherited trait. This disagreement invites a simple mathematical model to see how holobiont selection might operate and to assess its plausibility as an evolutionary force. This paper presents two variants of such a model. In one variant, juvenile hosts obtain microbiomes from their parents (vertical transmission). In the other variant, microbiomes of juvenile hosts are assembled from source pools containing the combined microbiomes of all parents (horizontal transmission). According to both variants, holobiont selection indeed causes evolutionary change in holobiont traits. Therefore, holobiont selection is plausibly an effective evolutionary force with either mode of microbiome transmission. The modeling employs two distinct concepts of inheritance, depending on the mode of microbiome transmission: collective inheritance whereby juveniles inherit a sample of the collected genomes from all parents, as contrasted with lineal inheritance whereby juveniles inherit the genomes from only their own parents. A distinction between collective and lineal inheritance also features in theories of multilevel selection. (shrink)

Elective mathematics has been an extra mathematics subject for pilot students of Eduardo Barretto Sr. National High School for quite some time now. Through this, many alumni testified how this helped them understand senior high school and college math. However, the teachers have also been struggling with the resources for specific areas of mathematics, such as Business Math, Statistics, Analytic Geometry, Trigonometry, and Calculus. When the pandemic hit the Philippines, contextualized learning material aligned with the Most Essential Learning Competencies (MELC) (...) helped elective mathematics teachers. The contextualized learning material was developed from April to August 2020 and was first validated in February 2021 by the students who participated in the pilot testing. However, following the due process, it was suggested that I revalidate the IDEA-formatted Analytic Geometry and Trigonometry instructional material. It examines Eduardo Barretto Sr. National High School mathematics teachers and SDO Calamba City experts' evaluation of the content's topics, objectives, concepts, directions, and activities and the format's prints, illustrations, design, and layout. Participants' perceptions of learning material were assessed using a 4-point Likert Scale survey. Hence, descriptive quantitative design. Participants were surveyed using a 4-point Likert Scale to assess their learning content impression. The findings reveal that the participants found the format and content of the developed learning material to be very satisfactory. The indicators "localized" and "can be done independently" were viewed as Fair and Satisfactory, respectively. The learning material was enhanced by localizing the activities and giving directions that could facilitate self-learning. (shrink)

The authors developed this textbook in response to an increasing interest in ethics, and a growing number of courses on this topic that are now being offered in educational leadership programs. It is designed to fill a gap in instructional materials for teaching the ethics component of the knowledge base that has been established for the profession. The text has several purposes: First, it demonstrates the application of different ethical paradigms (the ethics of justice, care, critique, and the profession) through (...) discussion and analysis of real-life moral dilemmas that educational leaders face in their schools and communities. Second, it addresses some of the practical, pedagogical, and curricular issues related to the teaching of ethics for educational leaders. Third, it emphasizes the importance of ethics instruction from a variety of theoretical approaches. Finally, it provides a process that instructors might follow to develop their own ethics unit or course. * Part I provides an overview of why ethics is so important, especially for today's educational leaders, and describes a multiparadigm approach essential to practitioners as they grapple with ethical dilemmas. * Part II deals with the dilemmas themselves. Ethical dilemmas written by the authors' graduate students bring readers face-to-face with the kinds of dilemmas faced by practicing administrators in urban, suburban, and rural settings in an era full of complexities and contradictions. * Part III focuses on pedagogy and provides teaching notes for the instructor. The authors discuss the importance of self-reflection on the part of both instructors and students, and model how they thought through their own personal and professional ethical codes as well as reflected upon the critical incidents in their lives that shaped their teaching and frequently determined what they privileged in class. (shrink)

We address Steel’s Programme to identify a ‘preferred’ universe of set theory and the best axioms extending ZFC by using his multiverse axioms MV and the ‘core hypothesis’. In the first part, we examine the evidential framework for MV, in particular the use of large cardinals and of ‘worlds’ obtained through forcing to ‘represent’ alternative extensions of ZFC. In the second part, we address the existence and the possible features of the core of MV_T (where T is ZFC+Large Cardinals). In (...) the last part, we discuss the hypothesis that the core is Ultimate-L, and examine whether and how, based on this fact, the Core Universist can justify V=Ultimate-L as the best (and ultimate) extension of ZFC. To this end, we take into account several strategies, and assess their prospects in the light of MV’s evidential framework. (shrink)

Dos filósofos dialogan sobre cómo definir en nuestros días la barbarie desde la filosofía política actual. Barajan para ello tres tipos de respuestas. La respuesta ilustrada es la que considera que la diversidad de concepciones del bien de nuestras sociedades es un hecho pernicioso para el desarrollo de la Humanidad, y que hay que imponer sobre ese batiburrillo de opiniones bárbaras la concepción sobre lo bueno más racional, la que en Occidente se propugna desde la Ilustración dieciochesca. La respuesta liberal, (...) por el contrario, acepta gustosa la pluralidad de concepciones morales y metafísicas de nuestras sociedades, y lo único que propone es evitar la barbarie haciendo que, en las cuestiones sobre cómo organizar nuestra sociedad, estas diferencias queden de lado y se intente encontrar un mínimo acuerdo entre todos. Por último, la respuesta postmetafísica sugiere aceptar que las cosmovisiones sobre el bien y el mundo no pueden quedar tan totalmente aparte de nuestros modos de organizar la sociedad como quiere el liberal; pero para evitar el conflicto bárbarico entre ellas, persigue hacer plausible sobre las demás una concepción concreta, que, a diferencia de la del ilustrado, aspiraría mucho más modestamente a sólo expandir un escepticismo para con el resto de nuestras propias creencias; autoironía que nos abriría al diálogo con las creencias de los demás y evitaría en ese juego de conversaciones la violencia de la imposición bárbara. (shrink)

This study aimed to determine the health practices among the secondary school teachers during the Covid-19 pandemic in Ichon National High School. This considered the socio - demographic profile of the teachers in terms of age, sex, civil status and teaching load and the extent of practice employed by the teachers in the said health dimensions. A total of 53 teachers from Ichon National High School participated as respondents in the evaluative method of research that consists in three parts questionnaires. (...) The statistical treatment used in the computation and analysis of gathered data to determine the socio-demographic profile of the respondents are the descriptive statistics such as frequency and percentage. As to the significance of health practices during COVID-19 pandemic, Kruskal Wallis and Mann-Whitney U test was used to analyze the significant differences on the extent of practices among the different health dimensions. The very high extent of the implementation on the health practices during COVID-19 pandemic shows that the teachers are frequently practiced the health practices. The highest mean in mental aspect is conclusive that teacher during the pandemic exert effort to stay healthy on this and other areas as well. It is recommended to conduct further study regarding on the health practices among the secondary school teachers. (shrink)

Comentaba en el Prólogo a la 1ª edición que nos cuesta distinguir las técnicas de los métodos y aceptar que la buena investigación clínica es la que se realiza con método riguroso. Este método reposa en cuatro pilares: que la pregunta o cuestión formulada sea relevante, que esté enunciada de manera precisa y operativa, que sea abordada o respondida con el mejor medio disponible en cada circunstancia, y que evite redundancias o repeticiones de cuestiones que ya han sido examinadas por (...) otros investigadores. Añadía que es imprescindible una dosis de curiosidad y de entusiasmo por lo que se examina. Como se ha dicho con frecuencia, el ensayo clínico es, entre los métodos de investigación clínica, el "patrón oro", el que, gracias a su característica inherente (la distribución aleatoria), está sujeto a menores posibilidades de sesgos. Esta consideración no ha cambiado. Sin embargo, mayor validez interna del método no implica mayor relevancia de los resultados obtenidos. Actualmente es común examinar protocolos de ensayos clínicos bien diseñados, cuyo "único" problema es que pretenden evaluar aspectos de escaso interés farmacológico, terapéutico, epidemiológico o sanitario. ¿Qué interés tiene la evaluación del quinto fármaco de una serie en una indicación para la que ya hay cuatro análogos que le han precedido en su desarrollo? ¿Qué interés tiene la evaluación de un nuevo hipocolesterolemiante o de un nuevo fármaco para la osteoporosis si no se conocen, respectivamente, el impacto de la hipercolesterolemia como factor de riesgo de cardiopatía isquémica o la epidemiología de las fracturas en mujeres postmenopáusicas en nuestro medio? En relación con estos ejemplos, tendría mucho más interés conocer los determinantes epidemiológicos y la historia natural de la cardiopatía isquémica en nuestro medio y conocer la epidemiología de las fracturas "espontáneas" y su impacto sobre la demanda asistencial; para ello serían de mucha utilidad métodos de investigación cuya validez intrínseca podría ser considerada "subóptima" en comparación con el ensayo clínico. En los últimos años ha irrumpido con fuerza en numerosísimas publicaciones el concepto de la "medicina basada en pruebas". Esta moda refleja en parte la importancia que de manera creciente reguladores e industria farmacéutica han concedido a los ensayos clínicos: se ha alcanzado un consenso global sobre la necesidad de demostrar la "eficacia" de los nuevos medicamentos por medio de ensayos clínicos controlados. De este modo, los organismos reguladores y autoridades sanitarias exigen ensayos clínicos como uno de los elementos necesarios para obtener el registro de un nuevo medicamento. Como consecuencia, se realizan y publican muchos más ensayos clínicos que antaño, y actualmente se pueden encontrar ensayos que sustentan la eficacia de la mayoría de los medicamentos disponibles en indicaciones específicas. Si hace unos años bastaba con examinar si había ensayos clínicos que demostraran la eficacia de un determinado medicamento antes de adoptarlo como uno de los de uso común (o de incluirlo en el formulario de un hospital), en la actualidad estas decisiones son más complejas, y se basan sobre todo en una consideración atenta de los objetivos, los métodos y los resultados de cada ensayo o de otros estudios destinados a evaluar eficacia, seguridad, conveniencia o comodidad y coste. Un buen clínico debe saber a la vez leer críticamente las publicaciones científicas y producir información relevante. Leer críticamente significa evaluar la pertinencia de los problemas investigados, los métodos aplicados y la interpretación de los resultados obtenidos. Producir información relevante implica saber identificar los problemas que deben y pueden ser objeto de investigación, formularlos, y ser protagonista (generalmente como parte de un equipo) de la elaboración del plan de investigación. En los últimos años se han publicado varios textos similares al que tiene en sus manos, todos ellos de gran calidad. El presente no pretende ser el más exhaustivo, sino sobre todo interesar a los profesionales sanitarios en el apasionante campo de la investigación clínica, en su sentido más amplio, estimulando la autonomía del lector para investigar un problema o una situación, y para aprender a leer las publicaciones científicas clínicas. Su lectura debe contribuir a que términos como "doble ciego", "p<0,05", "casos y controles", etc. dejen de ser fetiches-misterios, para convertirse en herramientas conceptualmente sencillas, útiles para la evaluación de la actividad asistencial. Esta nueva edición está muy ampliada respecto a la anterior. Se han reorganizado las generalidades sobre los objetivos y métodos de la investigación clínica, se han ampliado algunos aspectos del ensayo clínico, como el análisis de subgrupos, los aspectos estadísticos y éticos y las publicaciones sobre ensayos clínicos, se han añadido cuatro nuevos capítulos, sobre efectividad y eficacia, metaanálisis, ensayos en un solo paciente y farmacoeconomía, y el Glosario ha sido revisado y ampliado (sobre todo con términos de farmacocinética, desarrollo preclínico de fármacos, estadística y biotecnología genética), e incluye casi 750 términos. Para su elaboración me he basado en numerosos textos y diccionarios,a aunque he reformulado la mayoría de las definiciones y he optado por añadir en ocasiones algún comentario personal a muchas de ellas. Carles Vallvé ha escrito el capítulo sobre Normas de Buena Práctica Clínica. Agradezco asimismo las precisones y comentarios de Eulalia Dalmau, Javier Jiménez, Josep Maria Castel y Xavier Vidal, así como los comentarios a versiones anteriores de Fernando Antezana y Jorleny Rojas. Eduard Diogène me sugirió la idea de la portada, El sueño de la razón produce monstruos, que Goya comentaba así: " La fantasía abandonada de la razón produce monstruos imposibles: unida con ella es madre de las artes y origen de sus marabillas" La 1ª edición de este libro, que fue promovida por Zeneca, tuvo una amplia difusión, en España y en América Latina. AstraZeneca me propuso preparar esta 2ª edición del mismo modo abierto que en ocasión de la primera; su actual Director Médico Ramón Estiarte me ha ayudado en la selección de términos para el Glosario. A él y al anterior Director Médico de Zeneca, Manuel Martín, agradezco su idea inicial, su estímulo y ayuda, y las facilidades que han dado para la difusión de este libro. Joan-Ramon Laporte. (shrink)

Although the map of technology ethics is expanding, the growing subdomains within it may raise misgivings. In a recent and very interesting article, Sætra and Danaher have argued that the current dynamic of sub-specialization is harmful to the ethics of technology. In this commentary, we offer three reasons to diminish their concern about ethical proliferation. We argue first that the problem of demarcation is weakened if we attend to other sub-disciplines of technology ethics not mentioned by these authors. We claim (...) secondly that the logic of sub-specializations is less problematic if one does adopt mixed models (combining internalist and externalist approaches) in applied ethics. We finally reject that clarity and distinction are necessary conditions for defining sub-fields within ethics of technology, defending the porosity and constructive nature of ethical disciplines. (shrink)

This study aims to find out the factors that hinder students in learning Integrated Art Education. A descriptive research design was utilized in the conduct of the study. The researcher prepared a questionnaire with 15 closed-ended- questions that could be answered objectively. The study discovered that the students would learn more when they feel that they belong to a certain group. Interests in a subject also matter, the more you are interested in a particular subject, the more you will learn (...) the material. Parent support marks an impact on the student's interest in learning Arts. Therefore, personal interest in a subject must be given attention and managed properly. Parent's support also plays a vital role in reinforcing the students on what to pursue in order to maintain their motivation. (shrink)

En aquest article es presenten dues teories sobre la naturalesa del temps i s’analitzen objeccions que s’hi han presentat els darrers anys en el marc de la filosofia analítica. La primera sosté que el passat i el futur no són reals, i presenta el problema de com es poden expressar proposicions veritables sobre temps no presents. D’acord amb la segona teoria, per contra, tots els temps —present, passat i futur— són igual de reals, però això sembla implicar que el futur (...) sigui tan determinat i inexorable com el passat... L’autor clou amb una reflexió entorn de la manera de fer de la filosofia analítica i dels horitzons d’aquesta tradició. (shrink)

Amidst the challenges that teachers are facing nowadays, teachers resiliency in this new tough learning environment seemed to be an unexplored area. Thus, it is crucial to conduct studies that would explore factors that increase teachers resiliency particularly amidst teachers work-related stress and emotional exhaustion. This study explores the moderating effect of social support to self- efficacy and stress management strategies toward teachers resiliency employing descriptive-correlational with moderation design. teachers resiliency. The respondents were one hundred one (101) public elementary school (...) teachers who are currently associated with the four (4) public elementary schools in San Francisco District for the school year 2022-2023 using online survey questionnaire as the main instrument in gathering the data. The findings revealed that both teachers self-efficacy and stress management strategies have a significant relationship in teachers resiliency. This suggests that teachers must also be persistent in strengthening their self-efficacy and developing their stress management strategies to sustain their resiliency. Results also showed that social support effectively moderates the relationship between self-efficacy and teachers resilience. At the same time, it indicated that the higher self-efficacy of teachers was associated with a lower level of social support. Likewise, social support effectively moderates the relationship between stress management strategies and teachers resilience. Results also indicated that the higher level of stress management strategies was associated with lower level of social support. Individuals in the workplace especially supervisors and co-workers must consider providing their colleagues especially those with lower level of self- efficacy and stress management strategies with the necessary social support that they need to be resilient. (shrink)

This paper reconstructs Peter Carruthers’s arguments for criticizing the test focused on the metacognitive capacities of non-humans animals. It is possible to discuss metacognition or there are other mechanisms that being is used by animals in the metacognitive test? This paper offers an overview about the dispute about the metacognitive capacities(metaperception and metamemory) of the animals. The structure of this paper is the following: the first part presents the most relevant arguments that Carruthers offers to discuss and criticize the experiments (...) focused on animal metacognition. The second part it reconstructs the arguments against the Carruthers’s interpretation for explaining the metacognitive test. The third part it makes a balance between the Carruthers’s approach and his critic. Finally, the fourth part, in concluding that despite to the critics, the Carrtuhers’s arguments surpass these difficulties. (shrink)

Animal technique has occupied a marginal position in reflections on technique, and in the philosophical literature there is no strict definition of it. However, it is of great importance to understand the limits and the distinctive features of our own technique. This work argues that it is possible to establish a solid definition of animal technique based on two definitions of human technique (prosthetic notion of technique and material culture) and one particular dimension of human tools (cognitive tools). This paper (...) takes a naturalistic approach that enables to review different study cases focused on animals’ capacity to make and use tools. (shrink)

In pornography, standard modelling contracts often require a performer to surrender rights over their public image and sexual media in perpetuity and across mediums. Under these contracts, performers are unable to determine who accesses, for what duration, and under what conditions, their sexual media. As a result, pornography has been described by some performers as a “life sentence” - a phrase which, if true, violates some strong intuitions we share about the importance of autonomy in sexual activity. Using the framework (...) of “affirmative consent,” I argue that these contracts violate performers' rights to sexual autonomy, and ought therefore to be considered objectionable. Overall, I argue that the legal regimes we create have a strong impact on people’s lives, and more important than legislating individual outcomes, the type of infrastructure we build around people’s decisions has the potential to radically empower - or disempower - those engaged in sex work. (shrink)

El ambiente artificial en el que se despliega la vida en el planeta potencia un conjunto de interrogantes –algunos ya clásicos, otros novedosos– sobre los modos de existencia de los artefactos, sistemas y objetos técnicos que permean cada una de nuestras acciones. Parte importante de estos interrogantes se ocupa de las transformaciones que este ambiente artificial genera en la experiencia moral, política y cognitiva de los individuos, instituciones y sociedades. El Glosario de filosofía de la técnica elabora un mapa amplio, (...) ecléctico y heterogéneo, pero a la vez riguroso, a partir de las discusiones actuales en torno a la técnica en Latinoamérica y el ámbito hispanoparlante; abarca las discusiones canónicas dentro del campo de la filosofía de la técnica, pero también brinda un importante espacio a cuestiones emergentes, más recientes, con menos recorrido histórico, así como a conceptos que se desprenden de las agendas de indagación del ámbito local, muchas veces ausentes en las compilaciones impulsadas por el norte global y las modas académicas y editoriales. El panorama que presenta este volumen excede lo estrictamente filosófico (y sus distintas disciplinas) para incluir teoría de los medios, sociología, antropología, investigación en artes, letras y ciencias de la educación, entre otros abordajes posibles de la complejidad de la técnica como problema central de nuestros días. (shrink)

In this dissertation I offer a global and detailed reconstruction of the logic developed by Gottlob Frege throughout his career. Even though Frege's logic suffered profound modifications from his initial formulation in Begriffsschrift to its revised version in Grundgesetze, the significant differences between these two works have been rarely taken at face value. I not only argue that these differences exist, but I also explain how they should be understood in the light of the evolution of Frege's thought. First, I (...) suggest a new reconstruction of Begriffsschrift's logic, which amounts to a completely novel reading of its formal system—one that contradicts the core of modern historical studies. In particular, I defend that this logic is not—as it has been repeatedly said—a second-order logic and provide the following reasons. (1) The language is not properly a formal language. (2) In Begriffsschrift there is only one sort of quantification: quantification over arguments. (3) Begriffsschrift's logic does not have a semantics in the modern sense. Second, I offer an explanation of the reasons that drive the evolution of Frege's logic. The transition from Begriffsschrift to Grundgesetze has been seldom addressed and never fully explained. According to my historical analysis, the switch from Frege's position concerning logic in Begriffsschrift to his later conception—finally established in Grundgesetze—can be articulated through the adoption of the distinction between concept and object as the basic element of the formal system. This leads to a formalisation of the notion of concept, which in the end drives to Grundgesetze's notion of function. Finally, I put forward a global analysis of Grundgesetze's logic. In this work, Frege develops a formal system that resembles in many relevant ways a second-order one. I suggest a reconstruction of this formal system that allows us to compare it with Begriffsschrift's. In particular, I formulate precisely every rule of inference proposed by Frege and especially focus on the rules of substitution. Moreover, I reflect on several meta-logical results that can be drawn from this reconstruction. (shrink)

We examine the notion of cognitive artifact and its possible application to the animal technic. Although the issue of animal technic is not very much discussed, the case studies focused on the capacity of using and manufacturing tools suggest that some animals deploy cognitive skills. Could the tools employed by animals be considered genuine cases of cognitive artifacts? In this paper we propose a definition of “cognitive artifact” based on the notion of “proper function,” which allows us to develop a (...) gradual scale where we place different kinds of artifacts according to the prevalence of the cognitive function (in opposition to the prac-tical one). Applying this scale to the non-human sphere, we defend the idea that there exists a range of non-human technical phenomena of use and artifacts and tools manufacturing, and that some of this artifacts have an incipient proper cognitive function. In order to defend these theses, we examine the examples of the cobwebs, the nests and the honeycombs. (shrink)

Who is feminism for? The question reverberates frightfully in feminist discourse. Despite decades of theorizing that the unified feminist subject is an impossibility (given differences in race, class, sexuality, etc.), the question remains all too relevant in praxis—much to the detriment of the movement as a whole. Or at least, so argues Éléonore Lépinard in her new book, Feminist Trouble: Intersectional Politics in Post-Secular Times.

In this paper we consider the logics L(i,n) obtained from the (n+1)-valued Lukasiewicz logics L(n+1) by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong maximality among them are analyzed. We present a very general theorem that provides sufficient conditions for maximality between logics. As a consequence of this theorem, it is shown that L(i,n) is maximal w.r.t. CPL whenever n is prime. Concerning strong maximality (i.e. maximality w.r.t. (...) rules instead of only axioms), we provide algebraic arguments in order to show that the logics L(i,n) are not strongly maximal w.r.t. CPL, even for n prime. Indeed, in such case, we show that there is just one extension between L(i,n) and CPL obtained by adding to L(i,n) a kind of graded explosion rule. Finally, using these results, we show that the logics L(i,n) with n prime and i/n < 1/2 are ideal paraconsistent logics. (shrink)

This study focused on the adaptability and attitude of Grade 6 students in the Modular Learning Approach. This study aims to create a comprehensive review of the adaptability and attitude of elementary students in the Modular Learning Approach Especially. It seeks to describe and analyze the following: the profile of the respondents in terms of sex and education of the parents; the adaptability of the respondents toward the relationship between the student's profile in terms of their sex and educational attainment (...) of parents; the attitude of the respondent's significant relationship between sex and educational attainment. The researcher used the quantitative survey questionnaires to gather data from 128 Grade 6 students in five Elementary Schools in Bongabon, Nueva Ecija who enrolled during the School Year 2020-2021. The study revealed that the respondent's demographic profile in sex has no significant relationship to their adaptability and attitude in the modular learning approach. Yet the parents' educational attainment of the respondents has a significant relationship to adaptability in terms of learning assistance and support in the modular learning approach. The results further signified that parents' educational attainment is a basis for adaptability in modular learning. -/- . (shrink)

I critically discuss Dale Jacquette’s Frege: A Philosophical Biography. First, I provide a short overview of Jacquette’s book. Second, I evaluate Jacquette’s interpretation of Frege’s three major works, Begriffsschrift, Grundlagen der Arithmetik and Grundgesetze der Arithmetik; and conclude that the author does not faithfully represent their content. Finally, I offer some technical and general remarks.

El objetivo de este artículo es clarificar la noción de «vida auténtica» tal y como es descrita por Joan Roura-Parella en su última obra Tema y variaciones de la personalidad (1950). Por «vida auténtica» se entiende una vida autogobernada, que permite al individuo realizar su propia singularidad y, por tanto, preservar su autonomía y dignidad como persona. Una vida dominada por factores ajenos al propio individuo, sean cuales sean éstos, es una vida alienada, que no permite el desarrollo del (...) individuo en tanto la persona que es. Se señala la relevancia filosófica de la propuesta de Roura-Parella, que es la de ofrecer una justificación no-evidencial para una forma de vida cristiana, agapística. De acuerdo con Roura-Parella, una forma de vida basada en la entrega amorosa para con el prójimo está justificada en tanto que ésta es el resultado último de nuestra propia condición natural, constituyendo así un acto de afirmación personal y siendo, por tanto, condición necesaria para gozar de una vida auténtica — «la vida alcanza su hondo sentido al salirse de sí misma para darse a los demás» (Roura-Parella, Tema y variaciones de la personalidad, 1950, p. 229). Se señalan las diferencias y semejanzas de la propuesta de Roura-Parella con respecto a las de Miguel de Unamuno y Joaquim Xirau, autores que fueron cercanos a Roura-Parella y quienes, aunque partiendo de razonamientos distintos a los de Roura-Parella, también concibieron la entrega amorosa para con el prójimo como un acto de afirmación personal. (shrink)

El objetivo de este artículo es clarificar la noción de «vida auténtica» tal y como es descrita por Joan Roura-Parella en su última obra Tema y variaciones de la personalidad (1950). Por «vida auténtica» se entiende una vida autogobernada, que permite al individuo realizar su propia singularidad y, por tanto, preservar su autonomía y dignidad como persona. Una vida dominada por factores ajenos al propio individuo, sean cuales sean éstos, es una vida alienada, que no permite el desarrollo del (...) individuo en tanto la persona que es. Se señala la relevancia filosófica de la propuesta de Roura-Parella, que es la de ofrecer una justificación no-evidencial para una forma de vida cristiana, agapística. De acuerdo con Roura-Parella, una forma de vida basada en la entrega amorosa para con el prójimo está justificada en tanto que ésta es el resultado último de nuestra propia condición natural, constituyendo así un acto de afirmación personal y siendo, por tanto, condición necesaria para gozar de una vida auténtica — «la vida alcanza su hondo sentido al salirse de sí misma para darse a los demás» (Roura-Parella, Tema y variaciones de la personalidad, 1950, p. 229). Se señalan las diferencias y semejanzas de la propuesta de Roura-Parella con respecto a las de Miguel de Unamuno y Joaquim Xirau, autores que fueron cercanos a Roura-Parella y quienes, aunque partiendo de razonamientos distintos a los de Roura-Parella, también concibieron la entrega amorosa para con el prójimo como un acto de afirmación personal. (shrink)

La ciudadanía y lo político. Ciudadanía y crisis de la democracia liberal en un mundo en transformación es un texto provocador, que desafía directamente a las esferas de poder económico, político y social en el marco de la corrupción. Deja al descubierto las entrañas cancerígenas de una política enferma de poder, donde priman los intereses particulares o políticos sobre los intereses del pueblo. El libro es una lanza que atraviesa las profundidades que erosionan nuestra sociedad, realizando así un análisis riguroso (...) desde distintas aristas, que tienen un elemento común: la corrupción política. A lo largo de las páginas se ofrece un enorme panorama sobre el papel de la ciudadanía dentro de la sociedad, que reclama a gritos una revolución desalienante frente a la cleptoestructura. Es así como, el papel de la ciudadanía es el centro de la reflexión analítica que nos presenta Joan Lara Amat y León. (shrink)

When the cluster on “Sexual Expressions” began to take shape, one of the first people I thought of to serve as a referee was Joan Mason-Grant, given her longstanding philosophical and activist interest in pornography. It was with great sorrow that I learned, when I contacted her, that she had been diagnosed with a fast moving cancer. Joan was most interested to hear about this emerging “found cluster”; “it sounds like an interesting issue of Hypatia to look forward (...) to, but unfortunately my own academic work has had to be suspended” (May 17, 2009). She died just four days later. (shrink)

A critical review of a book on rape by Joan McGregor.

In 1937 Joan Robinson proposed that “when capitalism is rightly understood, the rate of interest will be set at zero and the major evils of capitalism will disappear”. A permanent zero rate would abolish capitalist profit except in limited cases, leaving nearly all output to be claimed by labour as wages. It would allow capital to be allocated on the basis of prospective social benefit rather than short-term profitability and a collateral basis that favours the wealthy. It would remove (...) some of the economic pressure to use resources unsustainably. So why not do this? I argue that the few available philosophical arguments for positive interest rates are unsatisfactory. Those who want a just and sustainable form of capitalism should target net zero for the interest rate. (shrink)

Bertrand Russell was never to forget the course he gave in Barcelona in the spring of 1920. In the bitter title-page of An Inquiry into Meaning and Truth (1940), after the legal ruling which had suspended him from teaching at City College, New York, he expressly mentions his lectures in Barcelona, along with those he had given at the Universities of Uppsala and Copenhagen and at the Sorbonne. He also alludes briefly to them in his Autobiography (Russell 1990, II, 143), (...) but their circumstances and import have received no attention to date. The aim of this paper is to bring to light the available information on this subject in the Russell Archives (McMaster University, Canada) and the papers left by Joan Crexells (1896-1926) and Eugenio d'Ors (1881-1954), the two Catalan philosophers behind Russell's visit, and to put forward an assessment of Russell's influence on Spanish philosophy. (shrink)

Among issues considered in contemporary ethics, apart from concepts such as good, value and justice, there is also the concept of care, discussed extensively in feminism. The article presents and analyses this ethical concept. It shows some problems with the translation of the English word ‘care’ into the Polish equivalent ‘troska’. The focus here, however, is mainly on the way of understanding the concept of care among feminist ethicists, such as Virginia Held, Nel Noddings, Joan Tronto, Diemut Bubeck, and (...) Sara Ruddick. For all of them, care is a relation, though they differ in their account of the specificity and meaning of this relation. (shrink)

The importation of Lacanian psychoanalysis into film theory in the 1970s and 1980s ushered in a new era of cinema scholarship and criticism. Figures including Raymond Bellour, Laura Mulvey, and Christian Metz are often considered the pioneers of applying Lacanian psychoanalysis in the context of film theory, most notably through their writings in Screen Journal. However, where French and British scholarship on Lacan and film reached its limits, American Lacanianism flourished. When Joan Copjec’s now classic essay “The Orthopsychic Subject: (...) Film Theory and the Reception of Lacan” was published in 1989, the trajectory of Lacanian film theory would become radically altered; as Todd McGowan recently put it, the “butchered operation” on Lacan committed by Mulvey and (quoting Copjec) the “Foucaultianization” of Lacan under the auspices of Screen Journal were finally indicted in one gesture through Copjec’s critique. Copjec and McGowan’s unique American view of Lacan marks a pivotal point in the convergence of psychoanalytic theory and cinema studies; by seeking to wrest Lacan from historist/deconstructionist theories of the subject, and by revisiting Lacan beyond the mirror stage, Copjec and McGowan can be said to have instantiated a resuscitation or even a renaissance of Lacanian theory in film studies in particular and in American scholarship more generally. In this essay, this renaissance of Lacanian theory is examined, focusing on the innovations these two American thinkers brought to psychoanalytic film theory and the multiple paths carved out into other disciplines that followed. First, a detailed summation of the contentions between screen theory and Copjec’s position is introduced, as well as McGowan’s assessment thereof. Then, the trajectory of psychoanalytic film theory after Copjec’s arrival is the focus, including the major innovations in her thought from cinematic subjectivity to sexual difference (most notably from Read My Desire) and the way her position spread to philosophy and ontology. Finally, the article identifies the limitations of Copjec’s and McGowan’s thought and seeks new possibilities through which we may continue to apply psychoanalysis to the cinema in the wake of these two important thinkers. L’importation de la psychanalyse lacanienne dans la théorie du film au cours des années 1970 et 1980 a apporté une nouvelle ère de recherche et de critique cinématographiques. Des figures comme Raymond Bellour, Laura Mulvey et Christian Metz sont souvent considérées comme étant les pionniers dans l’application de la psychanalyse lacanienne au contexte de la théorie du film, surtout dans leurs écrits pour le Screen Journal. Par contre, là où les recherches françaises et britanniques sur Lacan et la cinématographie ont atteint leurs limites, le lacanisme américain a prospéré. La publication en 1989 de « The Orthopsychic Subject: Film Theory and the Reception of Lacan », l’essai classique de Joan Copjec, a complètement changé la trajectoire de la théorie lacanienne du film; comme Todd McGowan l’a récemment exprimé, « l’opération massacrée » commise sur Lacan par Mulvey et (citant Copjec) la « Foucaultisation » de Lacan sous les auspices de Screen Journal avaient finalement été accusées d’un seul coup par la critique de Copjec. Le point de vue uniquement américain de Copjec et de McGowan sur Lacan marque un tournant dans la convergence de la théorie psychanalytique et des études cinématographiques. En cherchant à arracher Lacan des théories historicistes/déconstructivistes du sujet, et en revisitant Lacan au-delà du stade du miroir, Copjec et McGowan ont instancié une ressuscitation, voire une renaissance, de la théorie lacanienne dans les études cinématographiques en particulier et dans les études américaines en général. Dans cet article, cette renaissance de la théorie lacanienne est examinée, mettant l’accent sur les innovations que ces deux penseurs américains ont apportées à la théorie psychanalytique du film et les multiples chemins tracés dans d’autres disciplines subséquentes. Premièrement, un résumé détaillé des différends entre la théorie du film et la position de Copjec est présenté, ainsi que l’évaluation de McGowan à ce sujet. Puis, la trajectoire de la théorie psychanalytique du film après l’arrivée de Copjec est mise de l’avant, notamment les innovations importantes de sa pensée de la subjectivité à la différence sexuelle (particulièrement dans Read My Desire) et la manière dont sa position s’est propagée dans la philosophie et l’ontologie. Finalement, l’article identifie les limites de la pensée de Copjec et de McGowan et cherche de nouvelles possibilités à travers lesquelles nous pourrions continuer d’appliquer la psychanalyse au cinéma après ces deux grands penseurs. (shrink)

Joan McGregor argues that “colleges and universities should adopt as part of their core mission the development of skills of civil discourse” rather than engaging in the practice of restricting controversial speakers from making presentations on campuses. I agree with McGregor concerning the need for increased civil discourse. However, this does not mean universities should welcome speakers to publicly present any material they wish without restriction or oversight. In this paper, I make three main arguments: (i) Colleges and universities (...) have a duty to protect members of the campus community from the harm and exclusion resulting from hateful or harmful speech, in the same way that they must protect them from sexual assaults and concussions. (ii) In the vast majority of cases, this duty can be fulfilled by holding speakers to standards of discourse that prevail in academic debate, and insisting on a number of procedural requirements. (iii) We should be wary of conservative arguments framed in terms of free speech, because they can be deployed to undermine important functions of the university in a democratic society, namely, to teach students how to be discerning citizens, and to protect thinkers willing to be critical of the government and the ruling classes. (shrink)

Review of Joan Callahan, Reproduction, Ethics and the Law: Feminist Perspectives.

Technological developments involving robotics and artificial intelligence devices are being employed evermore in elderly care and the healthcare sector more generally, raising ethical issues and practical questions warranting closer considerations of what we mean by “care” and, subsequently, how to design such software coherently with the chosen definition. This paper starts by critically examining the existing approaches to the ethical design of care robots provided by Aimee van Wynsberghe, who relies on the work on the ethics of care by (...) class='Hi'>Joan Tronto. In doing so, it suggests an alternative to their non-principled approach, an alternative suited to tackling some of the issues raised by Tronto and van Wynsberghe, while allowing for the inclusion of two orientative principles. Our proposal centres on the principles of autonomy and vulnerability, whose joint adoption we deem able to constitute an original revision of a bottom-up approach in care ethics. Conclusively, the ethical framework introduced here integrates more traditional approaches in care ethics in view of enhancing the debate regarding the ethical design of care robots under a new lens. (shrink)

solicited by Joan Copjec; use Balibar to respond to Susan Moller Okin in my analysis of the tensions between feminism and multiculturalism.

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de (...) Lógica Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

This highly multidisciplinary collection discusses an increasingly important topic among scholars in science and technology studies: objectivity in science. It features eleven essays on scientific objectivity from a variety of perspectives, including philosophy of science, history of science, and feminist philosophy. Topics addressed in the book include the nature and value of scientific objectivity, the history of objectivity, and objectivity in scientific journals and communities. Taken individually, the essays supply new methodological tools for theorizing what is valuable in the pursuit (...) of objective knowledge and for investigating its history. The essays offer many starting points, while suggesting new avenues of research. Taken collectively, the essays exemplify the very virtues of objectivity that they theorize—in reading them together, the reader can sense various anxieties about the dangerously subjective in our age and locate commonalities of concern as well as differences of approach. As a result, the volume offers an expansive vision of a research community seeking a communal understanding of its own methods and its own epistemic anxieties, struggling to enunciate the key problems of knowledge of our time and offer insight into how to overcome them. -/- (Contributors: Alex Csiszar, Scott Edgar, Peter Galison, Ian Hacking, Sandra Harding, Moira Howes, Paolo Savoia, Judy Segal, Joan Steigerwald, and Alison Wylie). (shrink)

The paper leans on a movie cult from the 1960s, Blow-Up (1966) by Michelangelo Antonioni, of which a famous sequence is often mentioned, the one in which the protagonist, the photographer Thomas (considered here as a "conceptual character"), repeatedly enlarged the photographs he made in a park, in order to find an answer to the mystery surrounding the murder of a man: magnification which leads, on the one hand, to a gradual loss of definition of images, with the grain of (...) the picture becoming more and more evident, but also, on the other, in the emergence, from the very material of the print, of a fundamental detail that will help solve the mystery. What interests is the link between indicative referentiality and evidence documentary, between degrees of definition and authentication powers. The paper also analyzes the links that intertwine, in the film, between the photographs of Thomas (by Don McCullin) and paintings painted by another character of the movie, Bill (directed by Ian Stephenson), but also, outside the film, with all a series of examples from artistic production and visual culture of the time: very low definition images of the Kennedy assassination in Dallas (the famous Zapruder Film), the portrait of Lee Harvey Oswald directed by Sigmar Polke by simulating the halftone technique, the war photographs of Don McCullin and David Bailey's Fashion Photographs, Random Earths Studies by Mark Boyle and Joan Hills, Materialologies and Texturologies by Jean Dubuffet, as well as Zen for Film by Nam June Paik. Fimiani's text addresses also two contemporary installations which have tried to return to the issues from the photographic sequence of Antonioni's film: Blow-Up Blow-Up (2010) by Joan Fontcuberta and Portrait Landscape (from the Object Classifier series) (2015) by John Houck, an installation in which photograms of Blow-Up are analyzed through facial recognition software. (shrink)

This paper presents and discusses design studio outcomes developed in response to a studio brief linked to the Fun Palace Futures initiative of the Royal British Institute of British Architects (RIBA) in honour of architect Cedric Price and artist Joan Littlewood. The studio brief was collaboratively developed by the authors. Its core question was: How could the thoughts that guided the development and design of the Fun Palace – a project that was never built but is still today cited (...) as a model for thinking flexible and open architecture – be re-interpreted and renewed for the future? This line of thinking guided the initial and experimental research phase, during which students developed an understanding of what indeterminacy is or could be. The paper shows that through the translation of some of the essential principles of the Fun Palace project into pedagogical instruments, students were enabled to approach the questions of indeterminacy in an open and innovative manner. The paper argues that the use of a variety of media, which often went far beyond the conventional architectural pallet, and the introduction of media shifts were crucial in assisting the students in developing their own tools for creating a new kind of open and flexible architecture. The paper presents this pedagogic approach. We show that the conditions of indeterminacy, uncertainty, chance and change, hold potential for framing the design and creation of a new kind of dynamic architecture, and for initiating experimental architectural thinking in a design studio setting. (shrink)

Dance, as a mode of physical interaction, offers opportunities to care and be cared for, but this does not mean that dancers will, in fact, care. There may be no moral motivation underlying a lift, dip or intricate sequence of coordinated action. Choreographic scores may (knowingly or not) encourage merely perfunctory movements that are a poor simulacrum to care. Moreover, the caring that is expressed through dance need not transfer to other walks of life. I am not alone in knowing (...) spectacularly talented dancers whose behaviour off the dance floor is far from ethical – from the arrogant and petty to the flagrant abuse that plagues institutions of art and culture. This article considers how dance can illuminate both the acts and sentiments of care, conveying particular ethical orientations that trouble straightforward, absolute moral reasoning. The article frames an enquiry into the relation between ethics and aesthetics of care, drawn from feminist epistemologists Joan Tronto, Maurice Hamington, and Nel Noddings, as well as my own performance research on partnering. I frame a zone between technique and competence, foregrounding care in dance as both a technical and ethical issue. I will consider the necessary conditions by which dancing together can manifest care, rather than suggest blanketly that it always does or even that it should. To make this argument, I will describe and analyse Considered Care, a duet I created in the autumn of 2021 in collaboration with Boston Ballet. This performance research project provided the material from which to consider the concept of need, a condition of care in a dancing situation. I will conclude by considering the relationship between needs and trust in conceptualizing care within partnering. (shrink)

Several years ago, the poet & critic Joan Houlihan offered a scathing and hilarious indictment of a lot of postmodern poetry for using words in a way that treats them as meaningless (or, perhaps, renders them meaningless). She suggested that word choice in such poems doesn’t really matter, and that the poet could just as well have substituted in other words without any change in meaning or aesthetic qualities. I argue that she’s wrong about this. I offer an account (...) of how interpretation and meaning function in poems that use words in highly non-standard ways. In such poems, there are associations and implicatures that one can reasonably expect a suitably backgrounded reader to grasp, rescuing interpretation from being a purely subjective and arbitrary activity. (shrink)

Notes on and excerpted quotations from Eugene Halton’s theory of the self (and mind) as continuous with and involved in its objective surroundings as extensions of the self. These notes provide evidence for Halton’s multiple works as the earlier basis for what Russell Belk later called "the extended self" in 1988, for which he got credit while Halton’s original ideas were marginalized or excluded. In addition, Halton also developed some of these ideas as "critical animism," (see text) a predecessor to (...) what is now termed, "the new animism." First example: "We create environments that are extensions of our selves; that serve to tell us who we are, and act as role models for what we can become." Eugene Halton, quoted in Joan Kron, Home Psych, 1983. (shrink)

Confirming Robinson’s Statement? A Lakatosian Analysis of Keynes and his Immediate Orthodoxy Jesús Muñoz Abstract Was the Keynesian message alive during the second half of the XXth Century, or was it betrayed by his followers? This article in the fields of the history of economic thought and methodology contrasts the Scientific Research Programmes (SRPs), a Lakatosian concept, of Keynes in The General Theory of Employment, Interest and Money (TGT) with those of its immediate orthodox schools: Monetarism (MS), Neoclassical Synthesis (NS), (...) New Classical Macroeconomics – rational expectations – (RE) and General Disequilibrium (GD). The objective is to to assess the immediate impact of Keynes’s vision in economics. It can be concluded according to this comparison that Keynes’s bequeath was alive during the period between 1950 and 1980, but that it was accepted under different names. Many economists deny this statement. However it is hereby argued with the help of Lakatosian methodology that in both economic and philosophical terms the MS, NS, RE and GD SRPs are degenerative variants of Keynes's SRP. The Keynesian reasoning chain -a non self-regulated system, non neutrality on the part of money, organicism, non-ergodicity, historical time and uncertainty- is misunderstood and hence misapplied on the part of these deviant schools, or transformed into “bastard Keynesianism”, to quote Joan Robinson (Joan Robinson, 1975[1973], 125). In other words, Keynes’s economics is different from Keynesian economics as was firstly proposed by Axel Leijonhuvfud (Leijonhuvfud, 1968). The internal history of macroeconomics in those periods is undertaken, since it is is the rational reconstruction of the meaning of a SRP. Section 1 is an introduction to basic concepts related to philosophy of science and methodology, especially Lakatosian methodology, which can be skipped by the specialized reader. Section 2 is an analysis of Keynes’s hard core in his SRP, also being an introduction to the problem as it outlines Keynes’s thinking, Section 3 describes initial Post Keynesianism, which was faithful to the original message. Sections 4, 5, 6 and 7 outline the hard cores of Monetarists, Neoclassical Synthesis, New Classical Macroeconomics and General Disequilibrium, respectively. Section 8 is a comprehensive analysis of the differences between the mentioned paradigms, and hence concludes. References are listed at the end of the article. (shrink)

The philosopher René Descartes wrote the Compendium musicæ in 1618. Even though he was not known for his music production, he maintained a long correspondence around the subject in dialogue with Marin Mersenne, Constantjin Huygens, Isaac Beeckman and Joan-Albert Ban. However, his musical propositions appear as a marginal subject in his intellectual journey. To understand whether the musical theme relates to the development of his ideas, first, the organization of his correspondence about music and the citations to it in (...) his works was necessary, either in smaller texts or in the works published by the author. We analyzed the hypotheses about the forgetfulness of music in studies about the development of Descartes´ ideas. With these materials, we analyzed and historically contextualized the trajectory of the author's musical conceptions with the development of his main themes. Thus, it is possible to verify Descartes' musical dialogues with his own work and with his historical context. (shrink)

In my paper I make a summary assessment of the connection between Eugeni Crexells and Eugeni d'Ors and that of both of them with pragmatism. I organize it in three sections: 1. First, the philosophical formation of Crexells and its relation with D'Ors; 2. Eugeni d'Ors and pragmatism, and 3. Joan Crexells and pragmatism.

Predication is a lingual relation. We have this relation when a term is said (λέγεται) of another term. This simple definition, however, is not Aristotle’s own definition. In fact, he does not define predication but attaches his almost in a new field used word κατηγορεῖσθαι to λέγεται. In a predication, something is said of another thing, or, more simply, we have ‘something of something’ (ἓν καθ᾿ ἑνὸς). (PsA. , A, 22, 83b17-18) Therefore, a relation in which two terms are posited (...) to each other in a way that one is said (predicated) of the other is a predication. The term of which the other term is said is called a subject (ὑποκειμένον) and the other, which is said about the subject, is called the predicate. Thus, in a predication the predicate is predicated of the subject; given that being predicated is almost as the same as being said. The relation between being said and being predicated is so close that ‘if something is said of a subject both its name and its definition are necessarily predicated of the subject.’ (Cat., 5, 2a19-26) This, however, is true only about the second genera and not the accidents. a) Nature of relation in predication What is Aristotle’s theory about the nature of the relation in a predication? How does he fundamentally understand this relation? Phil Corkum distinguishes between predication logic and traditional term logic and argues that the relation between subject and predicate in Aristotle is of the latter kind. While in predicate logic, subjects and predicates have distinct roles, they have the same role in traditional term logic. In predication logic, subjects refer, but predicates characterize. Thereupon, a sentence expresses a truth if the object to which the subject refers is correctly characterized by the predicate. In traditional term logic, both subjects and predicates refer and a sentences expresses a truth if both name one and the same thing. He concludes that Aristotle ‘problematically conflates prediction and identity claims’ because while he thinks both subjects and predicates refer, he would deny that a sentence is true just in case the subject and the predicate name one and the same thing. Based on this, Corkum believes that Aristotle’s core semantic is not identity but the weaker relation of constitution, which is a mereological interpretation: ‘All men are mortal’ is true just in case the mereological sum of humans is part of the mereological sum of mortals. b) Aristotle’s theory of predication: one or two theories? Frank Lewis finds an inconsistent gap between the theory of predication in the Categories and that in the later books of the Metaphysics VII, 6. So too Joan Kung, Terry Irwin, Daniel Graham. c) Distinction of ‘being said of’ and ‘being in’ Owen enumerates the texts in which Aristotle’s distinction between ‘being said of’ and ‘being in’ is asserted: OI. 11b38-12a17; To., 127b1-4; Cat. 1a20-b9; 2a11-14; 2a27-b6; 2b15-17; 3a7-32; 9b22-24 d) Predication in Aristotle and the standard ‘S is P’ Marie De Rijk Lambertus thinks that the ‘S is P’ pattern is misleading when it comes to express predication in Aristotle. In his view, ‘The Aristotelian procedure should be described in terms of appositively assigning an attribute (κατηγορούμενον) to a substrate (ὑποκείμενον), rather than ascribing a predicate to a subject by means of a copula…. The comment should be considered an attribute which is said to fall to a substrate, without understanding this procedure in terms of sentence predication.’ e) Aristotle’s predication: bipartite or tripartite? It is a difficulty to make Aristotle’s theories of name-verb predication and tripartite predication consistent. The reason is that tripartite is not consistant with his name-verb structure based on which he says that the predicate term is the ‘verb.’ (20a31; 20b1-2; 16a13-5) The problem is that in a tripartite form like ‘Socrates is white’ we cannot take ‘is white’ as the verb because, based on Aristotle himself, no part of a verb can be significant itself. (16b6-7) However, his assertions about the equivalences between the two structures (OI. 12, 21b9-10; PrA. 51b13-16; Met., 1017b22-30) must mean that they are not inconsistent in his own view. Thus, as Allen Bāck points, ‘Aristotle seems to think that he has a single, consistent theory.’ The sense of saying or speaking as the root sense of rhema makes the relation between predication (saying something of something) and verb more interesting. The use of rhema in the sense of a long expression approves this. In Plato’s work (399ac) where Socrates claims that the name anthropos derives from anthron ha opopen (‘he who examines what he has seen’) we have an onoma from, or in place of, a rhema. 1) Subject The subject (ὑποκειμένον) is that of which another term is said or predicated. Aristotle’s own definition is of a much more philosophical value: ‘By subject I mean that which is expressed by an affirmative term (λέγω δὲ ὑποκείμενον τὸ κάταφάσει δηλούμενον).’ (Met., K, 1067b18) Throughout Aristotle’s work, three kinds of subjects can be found: possible, prime and absolute subject. a) Possible subject Those things that can take the position of a subject in a predication we call possible subjects, no matter they can or cannot take the position of predicate in any predication. All terms except the ultimate predicates are possible subjects because they can take the position of subject. b) Prime subject Those that in any predication can only take the position of a subject and not the position of a predicate are prime subjects. (Cat., 5, 3a36-b2; Met., Z, 1028b36-1029a1) This is the truest sense of subject and belongs only to substances. (Met., Z, 1029a1-2) In fact, ‘that which is not predicated of a subject, but of which all else is predicated’ is a substance. (Met., Z, 1029a7-9) In Categories, besides primary substances (Cat., 2, 1b3-6), individual qualities are also said not to be able to be said of anything else. (Cat., 2, 1a23-29) Aristotle’s examples are a certain ‘knowledge-of-grammar’ (τὶς γράμματικὴ) and ‘an individual white’ (τὸ τὶ λευκὸν). Thus, although substances are indeed in the truest sense individuals and, thereby, in the truest sense primary subjects, other individuals can take the position of subject as well. c) Absolute subject While substances are prime subjects of all other things, there is still something of which substances can be predicated and this predication is not an accidental predication: matter. (Met., Z, 1029a21-24) This predication is, indeed, the predication of a ‘form or this’ on matter and material substance. (Met., Θ, 1049a34-36) The only thing that is absolutely a subject, therefore, and can be a predicate is prime matter (πρώτη ὓλη). (Met., Θ, 1049a24-27) d) Subject and substance The most important thing in being a substance is being a subject: ‘It is because the primary substances are subjects for all the other things and all the other things are predicated of them or are in them, that they are called substances most of all.’ (Cat., 5, 2b15-17) And what is nearer to this position is more a substance as a species is more a substance than a genus.’ (Cat., 5, 2b7-8) e) Primary versus accidental subject A subject is a primary subject in a predication when the predicate is predicated of it as itself. In such a case, the subject is the subject of the predicate qua itself and not qua something else. A subject, on the one hand, is an accidental subject when it is not the primary subject of the predicate that is predicated on it. It means that a subject is an accidental subject when the predicate is predicated of it not qua itself but qua something else. An accidental subject is, therefore, anything other than a substance. 2) Predicate as universal It is evident from our discussion of kinds of subjects that except matter, primary substances (if we ignore both accidental predication and cases of absolute subjects) and other individuals, everything else can take the position of a predicate. Since primary substances are individuals, it results that everything except matter and individuals are capable to take the position of predicate. The immediate consequence of this is that the predicate must be a universal. When individuals cannot take the position of predicate, this position cannot be taken by any particular. Therefore, only universals can be predicated of others. Moreover, albeit universals can be a simple subject (for another universal), they are not prime subjects. The closeness of universal and predicate is to the extent that Aristotle differentiates universal from subject. (Met., Θ, 1049a27-30) 3) Categories or classes of predicates Aristotle distinguishes ten highest classes into one of which each predicate must necessarily fall: substance (or what a thing is), quality, quantity, relation, place, time, position, state, activity and passivity. (Cat., 4, 1b25-27; To., I, 9, 103b20- ; PsA., A, 22, 83b13-23) The substance counted among predicates must refer to secondary and not primary substances not only because Aristotle insists that primary substances cannot be predicated but also from his own examples of the category of substance: man and animal. (To., I, 9, 103b25) However, if a predicate be asserted of itself or its genus be asserted of it, the predicate signifies substance or what is; but if ‘one kind of predicate is asserted of another kind,’ it signifies one of the other nines. (To., I, 9, 103b30) These categories are so comprehensive that no predicate can remain outside them so that even non-being has as many senses as categories. (Met., M, 1089a26-30) a) That whether Aristotle’s categories are merely linguistic or fundamentally ontological is a so much controversial dispute. Some like G. E. R. Lloyd believe that ‘categories are primarily intended as a classification of reality … rather than of the signifying terms themselves.’ b) Although Aristotle’s categories have been historically regarded as a classification of predications, there are some recent commentators like Jonathan Barnes that think it is classifying predicates and not predications. 4) Kinds of predicates In his introduction of Categories, as J. W. Thorp truly points out , Aristotle distinguishes between the category of substance and the other categories using μὲν ... δὲ construction. This construction illustrates that beside tenfold classification of categories, there is an even more crucial differentiation between two kinds of predicates: substance or what is on the one hand and the other nine ones on the other hand: the distinction between what is predicated of the subject as what it is and what is predicated of it as an accident. Therefore, we have three kinds of classification - a twofold, a fourfold and a tenfold-complicatedly classifying the same thing, viz. the predicate. Predicates can be divided also to four kinds: property, definition, genus and accident. (To., I, 4, 101b11-20) A property is that predicate that is convertible with its subject and does not signify its essence. A definition is that predicate that is convertible with its subject and signifies its essence. It is a genus if it is not predicated convertibly and is contained in the definition of its subject. And it is an accident if it is neither convertible nor contained in the definition of its subject. (To., I, 8, ^103b3) All of these four kinds are among categories. (To., I, 9, 103b20) It seems that there might be some kind of relation between the twofold and the fourfold distinction: whereas genus and definition are predicated as what it is, accidents are not so predicated. There seems to be some rules that determine to each of these four kinds each predicate belongs. At To., IV, 123b30ff. Aristotle asserts: ‘If B has a contrary and A does not, then B does not belong to A as its genus.’ There is a dispute around per se accidents (τὰ καθ’ αὑτὰ συμβεβηκότα) (Topics., 102a18) whether they must be regarded as either of the four kinds or as a fifth kind. Barnes (1970) argued that they ‘do not fit at all neatly into the fourfold classification.’ He argues that based on the definition of accidents at A, 5, 102b4-5, they must be accidents but based on another definition, A, 5, 102b6-7, they cannot be accidents. He also defends the view that they are not properties. Barnes concludes: ‘This shows that the two definitions are not equivalent, and hence that the ‘predicables’ are not well-defined.’ Demetris J. Hadgopoulos defends the view that the two definitions of accidents are equivalent and per se accidents are properties. 5) Five types of predications We have five kinds of predications based on our division of subjects and our discussion of predicates: simple, primary (itself divided to substantial and accident), accidental (itself divided to primary and secondary), aoincidental and absolute predication. a) Simple predication. This is a predication in which a universal is predicated of either a particular or a universal subject. This sense of predication includes all other senses except the first kind of accidental predication. b) Primary predication. This is a predication in which a universal is predicated of a primary subject, namely a substance. A primary predication is of two kinds: i) Substantial predication. A primary predication in which the predicate is part of, or is included in, the definition of the subject. The universal that is the predicate here is the definition or the genus or the species or the diferentia of the subject. It is this predication that Aristotle calls a unity: ‘A statement may be called a unity … because it exhibits a single predicate as inhering not accidentally in a single subject.’ (PsA., B, 10, 93b35-37) It is only substantial predicates that can be predicated of each other: ‘Predicates which are not substantial are not predicated of one another.’ (PsA., A, 22, 83b18-19) Aristotle defines a substantial predication also in another way. A predication in which a higher genus is predicated on a lower genus, species, a substance or an individual, (or a species is predicated on an individual) is a substantial predication. Therefore, a substantial predication is a predication in a series that has individuals on one of its ends and a general category on its other end. In fact, only substantial predicates can be predicated of one another. (PsA., A, 22, 83b17-19) This series cannot be an infinite series because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) -/- ii) Accident predication. A primary predication in which the predicate is not part of, or is not included in, the definition of its subject. The universal that is the predicate here is the property or the accident of the subject. c) Accidental predication. This is a predication in which the subject is not a primary subject and its predicate is a substance. This predication is of two kinds: i) Primary accidental predication. This is a predication in which an accident is predicated of substance. Such a predication can go ad infinitum, which is inferable from Aristotle’s assertion that the secondary accidental predication cannot go ad infinitum. ii) Secondary accidental predication. It is a predication in which an accident is predicated of another accident. Such a predication, Aristotle asserts, cannot go ad infinitum because even more than two accidents cannot be combined. Now what is the meaning of Aristotle’s assertion that we cannot continue this ad infinitum? Does it mean that we cannot continue the predication ‘The musician is white’ and say ‘The white is Athenian?’ But why not? Or maybe he means that by adding any predication, we are still in a condition of predicating two accidents of a substance on each other. -/- As primary subjects, substances can also take the position of predicate though not essentially but accidentally. In propositions like ‘the white is a log’ or ‘That big thing is a log’ we observe substance taking the position of predicate but this is only accidentally: ‘When I affirm ‘the white is a log,’ I mean that something which happens to be white is a log- not that white is the subject in which log inheres (οὐχ ὡς τὸ ὑποκείμενον τῷ ξύλῳ τὸ λευκόν ἐστι), for it was not qua white or qua a species of white that the white (thing) came to be a log (οὔτε λευκὸν ὄν οὔθ᾿ ὃπερ λευκόν τι ἐγἐνετο ξύλον), and the white (thing) is consequently not a log except incidentally.’ (PsA., 22, 83a3-9) Aristotle compares this accidental use of substance in the position of predicate with the substantial use of it in the place of a subject: ‘On the other hand, when I affirm ‘the log is white,’ I do not mean that something else, which happens to be a log, is white (οὐχ ὃτι ἓτερόν τί ἐστι λευκόν, ἐκείνῳ δὲ συμβέβηκε ξύλῳ εἶναι), (as I should if I said ‘the musician is white,’ which would mean ‘The man who happens also to be a musician is white’); on the contrary, log is here the subject- the subject which actually came to be white, and did so qua wood or qua a species of wood and qua nothing else.’ (PsA., 22, 83a8-14) Aristotle asks us not to call propositions like ‘The white is a log’ a predication at all or at least call them accidental predication instead of simple (ἁπλως) predication. (PsA., A, 22, 83a14-17) An accidental predication, in which we have a substance in the place of predicate, is different from an essential predication in that while the subject of an accidental predication is said to be the predicate not by itself but as something different with which it coincides, the subject of an essential predicate is said to be the predicate by itself and not because it is something else: ‘Since there are attributes which are predicated of a subject essentially and not accidentally- not, that is, in the sense in which we say ‘That white (thing) is a man,’ which is not the same mode of predication as when we say ‘The man is white’: the man is white not because he is something else but because he is man, but the white is man because ‘being white’ coincides with ‘humanity’ within one subject. Therefore, there are terms such as are essentially subjects of predicates. (PsA., A, 19, 81a24-29) This capability of ‘non-essentially and only accidentally’ being a subject does belong, in fact, to all sensible things. (PsA., A, 27a32-36) d) Coincidental predication. this is a predication in which none of the subject and predicate are a substance or an individual. In this predication, one of the accidents of a substance or individual is predicated of one of the other accidentals of the same substance or individual. For example, when it is said that ‘The white is musical,’ there is an individual, say Socrates, for which both of white and musical are accidents. e) Absolute predication. This is a predication in which a form or a substance is predicated of a matter or a material substance. Some commentators like Loux and Lewis regarded this predication as close to accident predication, both based on inherence. As R.M. Dancy points out, these predications make Aristotle’s theory of predication immanentist: not only accident predications are explained by the immanence of accidents in substances, some of the substantial predications, which were not explained in Categories, are also explained by the immanence of form in matter. It is interesting that in this kind of predication, it is the predicate and not the subject, which is in the strictest sense substance. As the central books of Metaphysics claim, the form is the substance. Thus, in this predication, substance gets away from the sense of ὑποκείμενον. Corkum mentiones 68a19 as the only instance where Aristotle explicitly claims that a term may be predicated of itself, a passage that is, in Corkum’s view, problematic. 6) Demonstrable predicates Those predicates are demonstrable that are so related to their subjects that there are other predicates prior to them predicable of their subjects (ἔτι δ᾿ ἄλλος, εἰ ὧν πρότερα ἄττα κατηγορεῖται). (PsA., A, 22, 83b32-34) 7) Series of predications Since it is possible for a predicate to be itself the subject of another predication, we can have a series of predications in which the predicate of a predication is the subject of the next predication. This series has the following features: a) It has a limit (in number) (PsA., A, 22, 83b14-16) on the side of subjects: there are subjects that cannot themselves be predicated (PsA., A, 27, 43a39-41), which are, as we noted, prime subjects: particulars, i.e. prime substances and other individuals. (PsA., A, 19-22) Aristotle calls them ultimate (ὓστατον). (PsA., 21, 82a36-b1) b) It has a limit (in number of kinds) (PsA., A, 22, 83b14-16) also on the side of predicates: there must be predicates that cannot be subjects. (PsA., A, 19-22; PsA., A, 27, 43a36-39) Aristotle calls them primary (πρῶτον). (PsA., A, 21, 82b1-4) These are the highest categories or the highest genera of categories. (PsA., A, 22, 83b14-16) c) The series has an escalating shape from mere subjects at its downside to mere predicates at its upside. It is Aristotle himself whos uses the words up and down in this sense. (e.g. PsA., A, 22, 83b2-3) d) The predications that lie between lowest and highest ones must be finite in number. (PsA., A, 19-22 especially: 20, 82a21-35) These have subjects and predicates, each capable of both of the roles of being subject and being predicated. A result of this fitness is that neither demonstration can go to infinity nor everything is demonstrable, the two points Aristotle always insist on. e) The upward side includes the more universal ones and the downward the more particular ones. (PsA., 20, 82a21-23) f) It follows from the above features that ‘neither the ascending nor the descending series of predications … are infinite.’ (PsA., A, 22, 83b24-25) g) Reciprocation and convertibility. Except in case of terms (i.e. subjects and predicates) that are at each of the ends of series of predications, namely ultimates and primaries, it is possible to reciprocate (ἀντιστρέφειν) terms and convert the predication. (PsA., A, 19, 82a15-20) h) Antipredication. Antipredication means that in a predication (S is P), the subject becomes the predicate of its predicate (P is S) in the same category its predicate was predicated on it. For example, if P is in the category of quality, antipredication means that S be predicated of P in the category of quality. In other words, P is a quality of S and S is a quality of P. Aristotle rejects this. (PsA., A, 22, 83a36-b3) i) Self-predication versus other-predication. Aristotle distinguishes between a predication in which a term is said of itself and a predication in which a term is said of another. (Phy., Δ, 2, 209a31-33) j) Predicablity (Cat., 5, 3a36-b2): 1) Primary substances and individuals are not predicable. 2) Secondary substances are of two kinds: genus and species i) Genus is predicable able both of the species and of the individuals. ii) Species is predicable of the individual. 3) Differentiae are predicable both of the species and of the individuals. 8) Predication as classification a) Richard Patterson believes that Aristotle’s so repeated construction using hoper (estin A hoper B) in Topics (120a23 sq., 122b19, 26sq., 123a, 124a18, 125a29, 126a21, 128a35. Also in Posterior Analytics (83a24-30) (Brunschwig’s list. ‘expresses the fact that A is a kind of B (esti A B tis), that A is a species of the genus B.’ 9) Universal predication Aristotle defines universal predication (κατὰ παντὸς κατηγορεῖσθαι) as such: ‘wherever no instance of the subject (τῶν τοῦ ὑποκειμέμνου) can be found of which the other term cannot be asserted.’ (PrA., A, 24b27-29) In this predication, the subject is included in another as in a whole (ἐν ὃλῳ εἶναι) and the predicate is predicated of all of the subject (κατὰ παντὸς κατηγορεῖσθαι). (PrA., A, 24b26-27) Attach another discussion we had about ἐν ὃλῳ here. 10) Quantity of predication A predication, truly stated, has a quantity, which is the number of objects under the name of the subject of which the predicate is predicated. The quantity of subject can be stated in four ways: a. Indefinite: when the predicate belongs or does not belong to the subject without any mark to show to haw many of the particulars under the name of the subject it does or does not belong. E.g. ‘Man is white’; ‘Man is not white.’ (PrA., A, 24a20; OI., I, 7, 17b8-12) b. Universal quantity: When the predicate belongs to all or none of the subject. E.g. ‘Every man is animal’; ‘No man is animal.’ (PrA., A, 24a18-19; OI., I, 7, 17b5-6) The contrary of a predication of a universal quality is a predication of a universal quality. E.g. the contrary of ‘Every man is white’ is ‘No man is white.’ (OI., I, 7, 17b20-23) c. Particular quantity: When the predicate belongs (or does not belong) to some of the subject. E.g. ‘Some men are white’; ‘Some men are not white.’ (PrA., A, 24a19-20) d. Single quantity: when the subject is a proper name of only one object. E.g. ‘Socrates is white’; ‘Socrates is not white.’ The contrary of this predication is of a single quantity: ‘Socrates is not white.’ (OI., I, 7, 17b38-18a4) 11) Convertibility of predication. Some predications are convertible, that is, it is possible to change the place of subject and predicate in a true proposition so that the converted proposition remains true. This is supposed to mean that given the truth of a predication, the truth of the converted predication is inferable. The convert form of a predication depends on its quantity. a. Indefinite quantity: This predication has no strictly true convert because its quantity is not stated. b. Universal quantity: It can be converted in two ways: i) A negative universal can be converted to a negative universal in which the terms are changed. E.g. ‘No pleasure is good’ can be converted to ‘No good is pleasure.’ (PrA., A, 2, 25a5-8 and a14-19) ii) An affirmative universal can be converted to an affirmative particular in which the terms are changed. E.g. ‘Every pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a7-9) c. Particular quantity: If it is negative, it cannot be converted but if it is affirmative, it can be converted to an affirmative predication with particular quantity. E.g. ‘Some pleasure is good’ can be converted to ‘Some good is pleasure.’ (PrA., A, 2, 25a10-13 and a20-24) d. Single quantity: It cannot be converted. 12) Characteristics of relations between subject and predicate 1. A predicate is of a wider range than its subject. It is based on this fact that Aristotle: a) Prevents individuals to be predicate because there is nothing of which an individual be of a wider range. In other words, it is due to the fact that since an individual is only ‘one particular’ thing and, thus, cannot be of a wider extent than anything that Aristotle prevents them of being a predicate. Matthews, however, thinks we cannot use Socrates, a substance and an individual, in the place of predicate and say it of Socrates because ‘Socrates does not classify Socrates: it names him.’ b) Prevents differentia, species and things under species to be predicated of genus. (To., Z, 6, 144a27-) c) Prevents the species and the things under it to be predicated of the differentia. (To., Z, 6, 144b1-4) d) Also about the effect because it is wider than its subject. (PsA., B, 17, 99a) e) Each attribute is wider than every individual it is predicated on, though several attributes, collectively considered, might not be wider but exactly the substance of a thing. (PsA., B, 13, 96a32-b1) 2. The predicate of a predicate of a subject will be predicated of the subject too: ‘whenever one thing is predicated of another as of a subject, all things said of what is predicated will be said of the subject too.’ (Cat., 3, 1b10-15) In fact, it is due to its predication of the subject that it is predicated of its predicate. (Cat., 5, 2a36-b1) Moreover, what is not predicated of the predicate of a subject cannot be predicated of it as well. (PrA., A, 27, 43b22-27) Thus, what, for example, is not predicated of animal, cannot be predicated of man. 3. The predicate of a subject can be predicated of its predicates as well. (Cat., 5, 3a1-6) For example, you call the individual man grammatical and, thence, you call both a man and an animal grammatical. Nonetheless, the predicate of a subject belongs to it more properly than to its higher predicates. (PrA., A, 27, 43a27-32) 4. It is only the subject that can be distributed and not the predicate. (PrA., A, 27, 43b16-22; OI, I, 7, 17b12-16) Therefore, we can say e.g. ‘Every man is animal’ but we cannot say ‘Every man is every animal.’ 5. It is the reason of the relation between subjects and predicates, that is the reason of predication, which is the subject of inquiry. (Met., Z, 1041a20-24) In other words, since it is a meaningless inquiry to ask why a thing is itself (Met., Z, 1041a14-15), the only remaining meaningful inquiry is to ask why something is something else, i.e. to ask about the reason of predication. 6. A subject cannot categorize its predicate in the same category in which it is categorized by it. If e.g. A is a quality of B, B cannot be a quality of A. Therefore, there is no reciprocation in the same category. (PsA., A, 22, 83a36-39) 13) Characteristics of series of predications 1. A series of secondary accidental predication cannot go ad infinitum for not even more than two terms can be comnbined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. (Met., Γ, 1007b1-4) 2. Infinite series cannot be traversed in thought. (PsA., A, 22, 83b6-7) 3. The predications of genera on each other must be ended and cannot go to infinity because otherwise not only substances would not be definable but also a genus would be equal to one of its own species. (PsA., A, 22, 83b7-10) Therefore, a series of predication of genera on each other must be limited on both sides. There must be an upward limit in general categories as well as a downward limit in individual because they cannot be predicated of others. Whatever lies between these limits can both be predicated of others and others be predicated of them. (PrA., A, 27, 43a36-43) 4. The order of predicates matters: it makes a difference whether the series be ABC or BAC. (PsA., B, 13, 96b25-32) . (shrink)

Es conocido que el método de forcing es una de las técnicas de construcción de modelos más importantes de la Teoría de conjuntos en la actualidad, siendo el mismo muy útil para investigar problemas de matemática y/o de fundamentos de la matemática. El destacado matemático Joan Bagaria afirma lo siguiente sobre el método de forcing en su artículo "Paul Cohen y la técnica del forcing" (Gaceta de la Real Sociedad Matemática Española, Vol. 2, Nº 3, 1999, págs 543-553) : (...) "Aunque Cohen recibió la medalla Fields por su demostración de la independencia de la hipótesis del continuo y del axioma de elección, su contribución va mucho más allá de estos problemas. Su nuevo método, el forcing, no sólo ha permitido resolver un sinfín de problemas importantes en prácticamente todas las áreas de las matemáticas, si no que ha cambiado para siempre nuestra concepción de la matemática como ciencia". El objetivo principal del siguiente trabajo es estudiar el método de forcing describiendo algunas de sus aplicaciones (forcing de Cohen, forcing aleatorio, forcing de Mathias, forcing de Sacks, forcing de Silver, etc.), y ofreciendo una aproximación a sus fundamentos metamatemáticos. Se aspira que estas notas sirvan de apoyo para aprender dicho método. (shrink)

Providing the most thorough coverage available in one volume, this comprehensive, broadly based collection offers a wide variety of selections in four major genres, and also includes a section on film. Each of the five sections contains a detailed critical introduction to each form, brief biographies of the authors, and a clear, concise editorial apparatus. Updated and revised throughout, the new Fourth Edition adds essays by Margaret Mead, Russell Baker, Joan Didion, Annie Dillard, and Alice Walker; fiction by Nathaniel (...) Hawthorne, Ursula K. LeGuin, Anton Chekov, James Joyce, Katherine Mansfield, F. Scott Fitzgerald, William Faulkner, Alice Walker, Louise Erdrich, Donald Barthelme, and James McPherson; poems by John Donne, Robert Browning, Walt Whitman, Edwin Arlington Robinson, e.e. cummings, Langston Hughes, W.H. Auden, Philip Levine, and Louise Gluck; and plays by August Wilson, Marsha Norman, Wendy Wasserstein, and Vaclav Havel. The chapter devoted to film examines the relation of film to literature and gives the complete screenplay for Citizen Kane plus close analysis of a scene from the film. With its innovative structure, comprehensive coverage, and insightful and stimulating presentation of all kinds of literature, this is an anthology readers will turn to again and again. (shrink)